论文标题
部分可观测时空混沌系统的无模型预测
A Phase-Field Study on the Effects of Nanoparticles on Solidification and Grain Growth
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Nanoparticle reinforced alloys offer the potential of high strength, high temperature alloys. While promising, during rapid solidification processes, alloys suffer from nanoparticle clustering, which can discount any strength benefit. An open-source phase-field model is developed using PRISMS-PF to explore the impact of nanoparticles and clustering on alloy solidification. Heterogenous nucleation and grain boundary pinning are explicitly included, and a wide range of nanoparticle area fractions and nucleation rates are modeled. At low area fractions less than 0.05, particle clustering increases grain size between 15-45% compared to a random distribution. Our quantitative analyses inform a modified Zener grain size relationship that not only depends on nanoparticle size and area fraction, but also on the nucleation rate. Grain size first drastically decreases before plateauing at higher nucleation rates. Our simulations reveal a strong preference of nanoparticles pinning grain boundaries. Pinning fraction increases rapidly with nucleation rate before saturating between 0.85-0.90. Across the range of area fractions and nucleation rates considered, the random and clustered grain sizes each collapse to a simple analytical expression that depends only on nanoparticle radius and pinning fraction. Comparisons against experimental data reveal the expressions deduced from our analyses fit reported grain sizes better than classic Zener analysis. A simple model of strength and cost tradeoffs indicates nanoparticles can be a cost-effective way to improve alloy strength.
